Haze causes two effects: The primary effect is loss of contrast due to forward scatter. In addition, haze obscures i.e. reduces the effective clear aperture, which impacts the MTF of the optical system. As a general rule, obscuration of ~13% of the surface area of an optic will result in a noticeable degradation in image quality to the average observer or viewer. A more experienced observer will notice degradation with less of the clear aperture obscured. This is a significant amount of obscuration, but there is an impact.
For the amount of haze we generally see on used optics we use, the impact of haze is primarily loss of contrast due to forward scatter and for a given amount of haze on a lens is non-deterministic. Another way to say that is that you cannot tell what the effect is until you put it to use. It'll either work for you or it won't, and it's difficult to judge the impact just by observing the amount of haze (if it's slight.. if you can't see through the lens it's going to be pretty obvious that the imagery will be screwed up).
The only real trend is "the more haze, the greater the potential for adverse effects".
I have a recent example of this, with a Cornu Ontoscope that I just acquired and ran some dry plates through.
This is a stereo camera from the WW1 era, and in this pic the lenses appear fine. However, viewing through the open aperture showed the lenses had haze / contaminants on the optics. By visual appearance, they showed about the same amount of contaminants on both the left and right lenses. This provides a unique opportunity to remove all other variables to demonstrate this non-deterministic property of "haze" and other contaminants. Shot at the same time, with same lighting conditions, with optically-matched lenses, so the only real difference is the distribution of haze and contaminants on the lenses. However, scans reveal a significant difference in the image quality between the two lenses. Rest assured this image is fresh off the scanner without modification except to reduce the resolution so it can be uploaded here.
On the left, you can see a loss of contrast due to forward scatter (above and beyond the halation inherent in the dry plate).. there is low contrast in the lower right shadows of the big rock and rock wall on what is in fact a higher contrast emulsion.
On the right, there is significant loss of contrast as well as loss of high spatial frequency information i.e. details.
Again.. the haze / contaminants on the lenses visually appeared very similar. This is why I say it is non-deterministic, and you won't know until you try.
The rest of the story is that after seeing this, I stripped down the optics and cleaned them. Here is the result with the optics restored (ignore my poor focusing .. still tracking that issue down), and the camera taken back to shoot pictures in the same area the following day (so lighting is similar).
This is also a straight scan (same settings) with nothing done to the image except to scale down for posting here. Pretty obvious the contrast has significantly improved and the image quality is consistent on left and right.
So to recap...
1) Haze always degrades contrast and image quality. Below a certain threshold the effects are not noticeable.
2) You cannot determine the impact by visual inspection. It is a non-deterministic effect and varies on a case-by-case basis.
3) The only trend that can be inferred is: the more haze the more likely you'll have a problem.
4) If the degradation is noticeable, clean your optics carefully. You will see improvement.
One more comment:
Haze due to contaminants.. i.e. outgassing mentioned above, can be cleaned off with little more effort than getting to the lens surfaces to be cleaned. (by the way, very little attention is paid to this in the consumer world since cost is everything, but outside that industry optical designers pay very close attention to the problem).
Haze due to surface damage cannot be cleaned. The surface damage has to be polished off. Coated optics are actually easier to address, because the damage is typically limited to the coating. So to fix the coating is stripped off via pitch polishing, and then either left off or recoated.
We've all toyed with the idea of getting a hazy lens at low cost.. sometimes successfully, sometimes not. In the end, it's a crap shoot unless you have a way to address the problems caused by haze when you get the lens into your hands.
-Jason